4.2 Second Derivatives and Graphs

Checkpoint 1

In Figure C1 we show the graph of the function `htext[(] t text[)]=-t^3+12t`.

  1. For what range of `t` does the graph appear to be concave up?

  2. For what range of `t` does the graph appear to be concave down?

  3. Calculate the second derivative `h''text[(] t text[)]`, and use algebra to check your answers to parts (a) and (b).


Figure C1   Graph of `y=-t^3+12t`